






'''simple docstring'''





from __future__ import annotations

import math
def __UpperCAmelCase   (					A					:			list			,       A					:			list		)    ->   list:
			if len(A		) != 2 or len(a[0]		) != 2 or len(A		) != 2 or len(b[0]		) != 2:
						raise Exception('''Matrices are not 2x2'''		)
			UpperCAmelCase_      :       Optional[int]          =       [
			    [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
			    [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
			]
			return new_matrix
def __UpperCAmelCase   (					A					:			list			,       A					:			list		)    ->   Union[str, Any]:
			return [
			    [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]		)		)]
			    for row in range(len(A		)		)
			]
def __UpperCAmelCase   (					A					:			list			,       A					:			list		)    ->   List[Any]:
			return [
			    [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]		)		)]
			    for row in range(len(A		)		)
			]
def __UpperCAmelCase   (					A					:			list		)    ->   tuple[list, list, list, list]:
			if len(A		) % 2 != 0 or len(a[0]		) % 2 != 0:
						raise Exception('''Odd matrices are not supported!'''		)

			UpperCAmelCase_      :       Optional[Any]          =       len(A		)
			UpperCAmelCase_      :       Dict          =       matrix_length // 2

			UpperCAmelCase_      :       Optional[Any]          =       [[a[i][j] for j in range(A			,       A		)] for i in range(A		)]
			UpperCAmelCase_      :       Dict          =       [
			    [a[i][j] for j in range(A			,       A		)] for i in range(A			,       A		)
			]

			UpperCAmelCase_      :       List[Any]          =       [[a[i][j] for j in range(A		)] for i in range(A		)]
			UpperCAmelCase_      :       int          =       [[a[i][j] for j in range(A		)] for i in range(A			,       A		)]

			return top_left, top_right, bot_left, bot_right
def __UpperCAmelCase   (					A					:			list		)    ->   tuple[int, int]:
			return len(A		), len(matrix[0]		)
def __UpperCAmelCase   (					A					:			list		)    ->   None:
			print('''\n'''.join(str(A		) for line in matrix		)		)
def __UpperCAmelCase   (					A					:			list			,       A					:			list		)    ->   list:
			if matrix_dimensions(A		) == (2, 2):
						return default_matrix_multiplication(A			,       A		)

			UpperCAmelCase_    ,      UpperCAmelCase_    ,      UpperCAmelCase_    ,      UpperCAmelCase_      :       int          =       split_matrix(A		)
			UpperCAmelCase_    ,      UpperCAmelCase_    ,      UpperCAmelCase_    ,      UpperCAmelCase_      :       Optional[int]          =       split_matrix(A		)

			UpperCAmelCase_      :       Dict          =       actual_strassen(A			,       matrix_subtraction(A			,       A		)		)
			UpperCAmelCase_      :       Union[str, Any]          =       actual_strassen(matrix_addition(A			,       A		)			,       A		)
			UpperCAmelCase_      :       Any          =       actual_strassen(matrix_addition(A			,       A		)			,       A		)
			UpperCAmelCase_      :       str          =       actual_strassen(A			,       matrix_subtraction(A			,       A		)		)
			UpperCAmelCase_      :       str          =       actual_strassen(matrix_addition(A			,       A		)			,       matrix_addition(A			,       A		)		)
			UpperCAmelCase_      :       Optional[Any]          =       actual_strassen(matrix_subtraction(A			,       A		)			,       matrix_addition(A			,       A		)		)
			UpperCAmelCase_      :       Dict          =       actual_strassen(matrix_subtraction(A			,       A		)			,       matrix_addition(A			,       A		)		)

			UpperCAmelCase_      :       List[str]          =       matrix_addition(matrix_subtraction(matrix_addition(A			,       A		)			,       A		)			,       A		)
			UpperCAmelCase_      :       Dict          =       matrix_addition(A			,       A		)
			UpperCAmelCase_      :       Optional[Any]          =       matrix_addition(A			,       A		)
			UpperCAmelCase_      :       str          =       matrix_subtraction(matrix_subtraction(matrix_addition(A			,       A		)			,       A		)			,       A		)

			# construct the new matrix from our 4 quadrants
			UpperCAmelCase_      :       str          =       []
			for i in range(len(A		)		):
						new_matrix.append(top_left[i] + top_right[i]		)
			for i in range(len(A		)		):
						new_matrix.append(bot_left[i] + bot_right[i]		)
			return new_matrix
def __UpperCAmelCase   (					A					:			list			,       A					:			list		)    ->   list:
			if matrix_dimensions(A		)[1] != matrix_dimensions(A		)[0]:
						UpperCAmelCase_      :       Tuple          =       (
						    '''Unable to multiply these matrices, please check the dimensions.\n'''
						    F"Matrix A: {matrixa}\n"
						    F"Matrix B: {matrixa}"
						)
						raise Exception(A		)
			UpperCAmelCase_      :       List[Any]          =       matrix_dimensions(A		)
			UpperCAmelCase_      :       Optional[int]          =       matrix_dimensions(A		)

			if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
						return [matrixa, matrixa]

			UpperCAmelCase_      :       Optional[int]          =       max(*A			,       *A		)
			UpperCAmelCase_      :       Union[str, Any]          =       int(math.pow(2			,       math.ceil(math.loga(A		)		)		)		)
			UpperCAmelCase_      :       Optional[Any]          =       matrixa
			UpperCAmelCase_      :       Dict          =       matrixa

			# Adding zeros to the matrices so that the arrays dimensions are the same and also
			# power of 2
			for i in range(0			,       A		):
						if i < dimensiona[0]:
									for _ in range(dimensiona[1]			,       A		):
												new_matrixa[i].append(0		)
						else:
									new_matrixa.append([0] * maxim		)
						if i < dimensiona[0]:
									for _ in range(dimensiona[1]			,       A		):
												new_matrixa[i].append(0		)
						else:
									new_matrixa.append([0] * maxim		)

			UpperCAmelCase_      :       Optional[Any]          =       actual_strassen(A			,       A		)

			# Removing the additional zeros
			for i in range(0			,       A		):
						if i < dimensiona[0]:
									for _ in range(dimensiona[1]			,       A		):
												final_matrix[i].pop()
						else:
									final_matrix.pop()
			return final_matrix


if __name__ == "__main__":
						_UpperCamelCase						:						Optional[Any]  =					[
						    [2, 3, 4, 5],
						    [6, 4, 3, 1],
						    [2, 3, 6, 7],
						    [3, 1, 2, 4],
						    [2, 3, 4, 5],
						    [6, 4, 3, 1],
						    [2, 3, 6, 7],
						    [3, 1, 2, 4],
						    [2, 3, 4, 5],
						    [6, 2, 3, 1],
						]
						_UpperCamelCase						:						Optional[int]  =					[[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
						print(strassen(matrixa, matrixa))










'''simple docstring'''





from unittest.mock import patch

import pyspark

from datasets.packaged_modules.spark.spark import (
    Spark,
    SparkExamplesIterable,
    _generate_iterable_examples,
)

from ..utils import (
    require_dill_gt_0_3_2,
    require_not_windows,
)
def __UpperCAmelCase   (					A					:			Optional[int]			,       A					:			Optional[int]		)    ->   str:
			UpperCAmelCase_      :       List[Any]          =       []
			for part_id in partition_order:
						UpperCAmelCase_      :       Any          =       df.where(F"SPARK_PARTITION_ID() = {part_id}"		).collect()
						for row_idx, row in enumerate(A		):
									expected_row_ids_and_row_dicts.append((F"{part_id}_{row_idx}", row.asDict())		)
			return expected_row_ids_and_row_dicts
@require_not_windows
@require_dill_gt_0_3_2
def __UpperCAmelCase   (					)    ->   Any:
			UpperCAmelCase_      :       Any          =       pyspark.sql.SparkSession.builder.master('''local[*]'''		).appName('''pyspark'''		).getOrCreate()
			UpperCAmelCase_      :       List[str]          =       spark.range(1_0_0		).repartition(1		)
			UpperCAmelCase_      :       List[Any]          =       Spark(A		)
			# The id ints will be converted to Pyarrow int64s, so each row will be 8 bytes. Setting a max_shard_size of 16 means
			# that each partition can hold 2 rows.
			spark_builder._repartition_df_if_needed(max_shard_size=1_6		)
			# Given that the dataframe has 100 rows and each partition has 2 rows, we expect 50 partitions.
			assert spark_builder.df.rdd.getNumPartitions() == 5_0
@require_not_windows
@require_dill_gt_0_3_2
def __UpperCAmelCase   (					)    ->   str:
			UpperCAmelCase_      :       List[str]          =       pyspark.sql.SparkSession.builder.master('''local[*]'''		).appName('''pyspark'''		).getOrCreate()
			UpperCAmelCase_      :       Optional[Any]          =       spark.range(1_0		).repartition(2		)
			UpperCAmelCase_      :       int          =       [1, 0]
			UpperCAmelCase_      :       str          =       _generate_iterable_examples(A			,       A		)  # Reverse the partitions.
			UpperCAmelCase_      :       Optional[Any]          =       _get_expected_row_ids_and_row_dicts_for_partition_order(A			,       A		)

			for i, (row_id, row_dict) in enumerate(generate_fn()		):
						UpperCAmelCase_    ,      UpperCAmelCase_      :       int          =       expected_row_ids_and_row_dicts[i]
						assert row_id == expected_row_id
						assert row_dict == expected_row_dict
@require_not_windows
@require_dill_gt_0_3_2
def __UpperCAmelCase   (					)    ->   Union[str, Any]:
			UpperCAmelCase_      :       str          =       pyspark.sql.SparkSession.builder.master('''local[*]'''		).appName('''pyspark'''		).getOrCreate()
			UpperCAmelCase_      :       List[Any]          =       spark.range(1_0		).repartition(1		)
			UpperCAmelCase_      :       Optional[int]          =       SparkExamplesIterable(A		)
			assert it.n_shards == 1
			for i, (row_id, row_dict) in enumerate(A		):
						assert row_id == F"0_{i}"
						assert row_dict == {"id": i}
@require_not_windows
@require_dill_gt_0_3_2
def __UpperCAmelCase   (					)    ->   Union[str, Any]:
			UpperCAmelCase_      :       Dict          =       pyspark.sql.SparkSession.builder.master('''local[*]'''		).appName('''pyspark'''		).getOrCreate()
			UpperCAmelCase_      :       Dict          =       spark.range(3_0		).repartition(3		)
			# Mock the generator so that shuffle reverses the partition indices.
			with patch('''numpy.random.Generator'''		) as generator_mock:
						UpperCAmelCase_      :       Any          =       lambda A		: x.reverse()
						UpperCAmelCase_      :       Dict          =       _get_expected_row_ids_and_row_dicts_for_partition_order(A			,       [2, 1, 0]		)

						UpperCAmelCase_      :       List[Any]          =       SparkExamplesIterable(A		).shuffle_data_sources(A		)
						assert shuffled_it.n_shards == 3
						for i, (row_id, row_dict) in enumerate(A		):
									UpperCAmelCase_    ,      UpperCAmelCase_      :       Dict          =       expected_row_ids_and_row_dicts[i]
									assert row_id == expected_row_id
									assert row_dict == expected_row_dict
@require_not_windows
@require_dill_gt_0_3_2
def __UpperCAmelCase   (					)    ->   int:
			UpperCAmelCase_      :       Tuple          =       pyspark.sql.SparkSession.builder.master('''local[*]'''		).appName('''pyspark'''		).getOrCreate()
			UpperCAmelCase_      :       int          =       spark.range(2_0		).repartition(4		)

			# Partitions 0 and 2
			UpperCAmelCase_      :       int          =       SparkExamplesIterable(A		).shard_data_sources(worker_id=0			,       num_workers=2		)
			assert shard_it_a.n_shards == 2
			UpperCAmelCase_      :       Union[str, Any]          =       _get_expected_row_ids_and_row_dicts_for_partition_order(A			,       [0, 2]		)
			for i, (row_id, row_dict) in enumerate(A		):
						UpperCAmelCase_    ,      UpperCAmelCase_      :       Dict          =       expected_row_ids_and_row_dicts_a[i]
						assert row_id == expected_row_id
						assert row_dict == expected_row_dict

			# Partitions 1 and 3
			UpperCAmelCase_      :       Tuple          =       SparkExamplesIterable(A		).shard_data_sources(worker_id=1			,       num_workers=2		)
			assert shard_it_a.n_shards == 2
			UpperCAmelCase_      :       List[str]          =       _get_expected_row_ids_and_row_dicts_for_partition_order(A			,       [1, 3]		)
			for i, (row_id, row_dict) in enumerate(A		):
						UpperCAmelCase_    ,      UpperCAmelCase_      :       Union[str, Any]          =       expected_row_ids_and_row_dicts_a[i]
						assert row_id == expected_row_id
						assert row_dict == expected_row_dict







@require_not_windows
@require_dill_gt_0_3_2
def __UpperCAmelCase   (					)    ->   Any:
			UpperCAmelCase_      :       List[Any]          =       pyspark.sql.SparkSession.builder.master('''local[*]'''		).appName('''pyspark'''		).getOrCreate()
			UpperCAmelCase_      :       List[str]          =       spark.range(1_0_0		).repartition(1		)
			UpperCAmelCase_      :       int          =       Spark(A		)
			# Choose a small max_shard_size for maximum partitioning.
			spark_builder._repartition_df_if_needed(max_shard_size=1		)
			# The new number of partitions should not be greater than the number of rows.
			assert spark_builder.df.rdd.getNumPartitions() == 1_0_0


